write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the…

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } \\)\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } = \\sin 60 ^ { \\circ } \\)\n\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression.)\n\nfind the exact value of the expression.\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } = \\square \\)\n\n(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

write the expression as the sine, cosine, or tangent of an angle. then find the exact value of the expression\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } \\)\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } = \\sin 60 ^ { \\circ } \\)\n\n(type an exact answer, using \\( \\pi \\) as needed. use integers or fractions for any numbers in the expression.)\n\nfind the exact value of the expression.\n\n\\( \\sin 5 ^ { \\circ } \\cos 55 ^ { \\circ } + \\cos 5 ^ { \\circ } \\sin 55 ^ { \\circ } = \\square \\)\n\n(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Answer

Explanation:

Step1: Use the sine addition formula

The formula for (\sin(A + B)=\sin A\cos B+\cos A\sin B). Here (A = 5^{\circ}) and (B=55^{\circ}), so (\sin5^{\circ}\cos55^{\circ}+\cos5^{\circ}\sin55^{\circ}=\sin(5^{\circ}+ 55^{\circ}))

Step2: Calculate the sum of angles

(5^{\circ}+55^{\circ}=60^{\circ}), so (\sin(5^{\circ}+55^{\circ})=\sin60^{\circ})

Step3: Find the value of (\sin60^{\circ})

We know that (\sin60^{\circ}=\frac{\sqrt{3}}{2})

Answer:

(\frac{\sqrt{3}}{2})